Graphing Linear Equations Unit Test

Question

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Question
Use the image to answer the question.

An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma negative 2 right parenthesis and left parenthesis 1 comma 3 right parenthesis.

Use the graph to derive the equation of the line in slope-intercept form.

(1 point)
y=
x-

Answer 1

To derive the equation of the line in slope-intercept form (which is \(y = mx + b\)), we need to find the slope (m) and the y-intercept (b) of the line.

1. Identify two points on the line: You've given that the line passes through the points (0, -2) and (1, 3).

2. Calculate the slope (m) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Here, \((x_1, y_1) = (0, -2)\) and \((x_2, y_2) = (1, 3)\). \[ m = \frac{3 - (-2)}{1 - 0} = \frac{3 + 2}{1} = \frac{5}{1} = 5 \]

3. Identify the y-intercept (b): Since the line passes through the point (0, -2), the y-intercept (b) is -2.

Putting it all together, the slope-intercept form of the line is: \[ y = 5x - 2 \]

So the answer is: \[ y = 5x - 2 \]